Liquid immersion tank

Compare buoyancy and resistance

Choose liquid, shape, material, diameter or edge length, and drop height. Drop height is the initial gap from the body’s lowest point to the fluid surface; the full 2–80 cm input is used. Drop starts the experiment; Pause and Step 0.1 s allow inspection. Playback settings offer 1×, 5× and 20× time factors. Input changes discard the previous run. Hidden tools pause without catching up; reduced motion starts paused. Floor contact is assumed not to seal the body against the liquid, so ideal hydrostatic buoyancy remains present.

Volume and forces

The square tank is 42 × 42 cm with an initial liquid depth of 40 cm. Its area is A = 0.1764 m². The instantaneous surface z solves A(z − 0.4) = Vsub(y,z), conserving the liquid volume. A sphere uses its exact spherical-cap volume; cubes, upright cylinders and discs use constant cross-sections. Disc thickness is max(0.04D, 1 mm), cylinder height is 1.5D. The streamlined body has 0.7 times a sphere’s volume, height 1.1D and an explicitly approximate height-based immersion rule.

Up is positive: weight −mg, buoyancy ρgVsub, resistance −bv −qv|v|, plus a non-negative support force on the floor. For a resting sinking body, support balances weight minus buoyancy. Floating equilibrium has Vsub/Vbody = ρbody/ρliquid and includes the resulting level rise. Neutral buoyancy refers to equal densities, not a uniquely selected resting depth. g = 9.81 m/s². The table includes all vertical forces in N. Arrow lengths are scaled and limited for legibility; compare their numeric values. A dashed locator around a very small body is not its physical diameter.

Dynamics and limitations

The body remains upright and moves only vertically. Liquid resistance blends a Stokes-style term b = f·3πμL (factor 0.4 for the streamlined body) with q = f·ρCdAproj/2 plus an air term for the dry fraction. Cd and material properties are fixed representative teaching values, not precision data. L is the model characteristic diameter/edge (0.9D for the streamlined body). The linear rule for non-spherical bodies and the streamed shape’s volume rule are approximations. Re = ρ|v|L/μ is diagnostic, not an automatic switch of drag law.

Resistance is integrated implicitly to remain stable in viscous fluids; substeps resolve surface restoring forces. Floor impact uses restitution 0.1. Floating rest is detected only near the independently calculated equilibrium with speed below 0.0001 m/s and position tolerance max(0.1 μm, body height × 0.00001). There is no arbitrary time-based claim of rest. Added mass, fluid waves, impact splashes, rotation, surface tension and non-Newtonian behaviour are excluded; the surface follows volume conservation instantly. This is a one-body illustrative model, not CFD.

References: Archimedes and floating fraction; drag and terminal speed. The volume-coupled tank and numerical scheme are explicit tool modelling choices.

Reset restores all defaults. Only exact input text, material/shape/liquid selections and playback factor are retained; positions, motion and results are never saved. After the first run, valid parameter changes immediately show a new paused starting state. Resume starts its motion.